A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks

Abstract Stress activates a complex network of hormones known as the hypothalamic–pituitary–adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone‐secreting glands. The mass changes are caused by HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia, and postpartum. Dysregulation occurs for a wide range of parameters and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland‐mass dynamics may play an important role in the pathophysiology of stress‐related disorders.

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REFEREE REPORTS
Reviewer #1: This manuscript develops a new model for the Hypot halamic-Pit uit ary-Adrenal (HPA) set of hormones. The hormones (except cort isol) ret urn to normal baseline levels despit e prolonged st ress. However, temporal responses of all hormone levels aft er CRH inject ion (called the CRH test ) differ from normal. Exist ing mat hemat ical models do not incorporat e the cell masses of glands producing these hormones and cannot reproduce the time courses following the CRH test at early and int ermediat e phases of recovery aft er st ress wit hdrawal. The aut hors show that including the effect ive gland masses and their regulat ion in the model capt ures the experiment ally observed behaviors, specifically the persist ence of blunt ed ACTH response to the CRH test . Finally, the st rengt h of Glucocort icoid Recept or (GR)-mediat ed negat ive feedback cont rol in HPA resilience during prolonged st ress and the benefit s of mass changes are examined. This is a clearly writ ten, int erest ing manuscript explaining the workings of an import ant physiological syst em deregulat ed in many humans for various reasons. It also ext ends the concept of dynamic compensat ion from Karin et al. (2016) to a new physiological syst em, suggest ing the generalit y of the concept . I would like to recommend publicat ion once a few minor comment s can be considered.
Minor point s: (1) There is a st at ement in the Int roduct ion that epigenet ic regulat ion of GR sensit ivit y cannot explain the CRH test result s. Has this been shown in any of the references cit ed? If not then add a reference to the Methods section showing epigenetic regulation is insufficient to capture the experimental data.
(2) Instead of cell masses, the production rate per each cell could increase to give the same outcome. That is, one could imagine b_2(t) and b_3(t) being time-dependent while C and A being constant. This does not happen, which probably suggests that there are some constraints on hormone output per individual cell. Can this be discussed a bit?
(3) Fig. 2b: when showing the cell masses, it may be useful to show the control cell masses somehow as well (preferably in gray). Also, label those rows "Cell masses".
(4) The cortisol baseline depends on very few parameters -but still depends on k-s and w-s. Also, this is the only hormone for which the baseline does not return to normal during prolonged stress. Why? In principle, could there be regulatory mechanisms to also push cortisol levels back to baseline? Why is it OK for human physiology to have high cortisol, but not OK to have abnormal levels of the other hormones?
(5) What would happen if both cell masses would depend on the same single hormone (either only x1 or only x2)?
Reviewer #3: This is a very well written manuscript that suggests an explanation for data showing disconnection between ACTH secretion and CORT secretion following chronic stress. The beauty of the paper is the simplicity of the hypothesis: that everything can be explained by dynamic changes in the mass of the hormone-secreting cells. As demonstrated, if these changes occur on different slow time scales, then other features of the network (particularly negative feedback of cortisol) ensure that observations on hormone secretion levels that have been reported experimentally under a variety of stress-related conditions are replicated. No sensitivity analysis is needed, this is a very robust network response if one incorporates slow dynamic changes in cell mass. The work is a nice example of how a simple mathematical model can be used to explain ubiquitous data. I have only a few comments: 1) AVP is never mentioned. This is strange, since AVP is co-released with CRH from hypothalamic neurons and has a strong effect on corticotroph activity. I realize that much of the paper focusses on data from CRH tests (which don't involve AVP), but the physiological stimulatory role of AVP should at least be mentioned when the HPA axis is discussed. ) that could explain other data including pathways to diabetes. Again, a main focus was on dynamic changes in the mass of the hormonesecreting (insulin in this case) cells. I get the feeling that the authors don't know about this work, which is based on dynamic compensation of cell mass (though I am not sure if that language was used). The authors only cite one of their own papers on the insulin-glucose system, which is also from 2016. Clearly, these other papers are relevant and should be cited and discussed as earlier models exhibiting dynamic compensation in an endocrine system.
3) The Fig. 1 caption incorrectly states that the thicker curves are control.  This process, however, cannot explain, on its own, the observed dysregulation. The reason is that GR resistance does not break the association between ACTH and cortisol: GR resistance should cause both ACTH and cortisol levels to increase, in contrast to the observed ACTH blunting.
We  Figure S1). This mechanism also does not result in blunted ACTH responses (in fact, it sensitizes ACTH responses), and there is no mismatch between cortisol and ACTH after recovery from prolonged stress. The reason for this is that varying GR sensitivity does not disrupt the correspondence between ACTH levels and responses to cortisol levels, so when ACTH responses are blunted, cortisol levels are low, and vice versa.
(2) Instead of cell masses, the production rate per each cell could increase to give the same outcome.

That is, one could imagine b_2(t) and b_3(t) being time-dependent while C and A being constant. This does not happen, which probably suggests that there are some constraints on hormone output per individual cell. Can this be discussed a bit?
We thank the reviewer for this comment. We addressed this in a new discussion session, where we discuss hormone secretion per cell, as well as mechanisms for increase in cell mass (page 17): We considered here changes in hormone production due to changes in total cell mass, rather than in intrinsic per-unit-biomass production rate parameters b 2 and b 3 . These parameters could, in principle, also change as a function of time, although they may be limited by constraints on secretory capacity per unit biomass. Changes in production due to total cell mass changes have been well documented in (3) Fig. 2b: when showing the cell masses, it may be useful to show the control cell masses somehow as well (preferably in gray). Also, label those rows "Cell masses".
We fixed this according to the suggestions of the reviewer.

(4) The cortisol baseline depends on very few parameters -but still depends on k-s and w-s. Also, this
is the only hormone for which the baseline does not return to normal during prolonged stress. Why?

In principle, could there be regulatory mechanisms to also push cortisol levels back to baseline? Why is it OK for human physiology to have high cortisol, but not OK to have abnormal levels of the other hormones?
We thank the reviewer for this comment, which made us revise the paragraph in the results which analyzes the compensation properties of cortisol. We discuss this now in the revised

paragraph (page 15):
Cortisol in the present analysis is the only HPA hormone that does not return to baseline after prolonged stress input. This may correspond to its physiological role as a stress response hormone, with multiple physiological end-points, including modulation of immunity, metabolism, and behavior (McEwen, 1998). Cortisol therefore adjusts these end-points according to averaged stress levels, allowing ongoing response as long as stress persists. Together with the persistent responsiveness of cortisol to stress input u, the circuit allows cortisol level to be independent on almost all other parameters, including the hormone production rates per unit biomass ( 2 , 3 ) or removal rates ( 2 , 3 ), as well as the rates of the proliferation and removal of the adrenal cortex cells, and .
This robustness is due to the ability of the functional masses to grow and shrink to buffer changes in these parameters. It allows cortisol to respond precisely to chronic stress input despite physiological variations in many of the circuit parameters. We also refer to this SI section in the main text in the results (page 14).
"We also tested other putative circuit designs in which the hormones control mass changes in alternative ways, and find that the interactions considered here are among the very few designs that provide the observed HPA behavior (Appendix Section 3)."

Reviewer #3:
This is a very well written manuscript that suggests an explanation for data showing disconnection between ACTH secretion and CORT secretion following chronic stress. We thank the reviewer for this endorsement.
1) AVP is never mentioned. This is strange, since AVP is co-released with CRH from hypothalamic neurons and has a strong effect on corticotroph activity. I realize that much of the paper focusses on data from CRH tests (which don't involve AVP), but the physiological stimulatory role of AVP should at least be mentioned when the HPA axis is discussed.
We agree with the reviewer, and we now addressed this comment by adding a new paragraph in the discussion which discusses the role of AVP in the context of our model (page 16): Another potentially important extension of the model will be to incorporate hypothalamic neuropeptides that modulate the secretion of ACTH, such as arginine vasopressin (AVP  3) The Fig. 1  Thank you for sending us your revised manuscript . We have now heard back from the two reviewers who were asked to evaluat e your st udy. As you will see the reviewers are sat isfied wit h the modificat ions made and think that the st udy is now suit able for publicat ion.
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